Abstract
We are mainly concerned with the partially linear additive model defined for a measurable function by
where and
are vectors of explanatory variables,
is a vector of unknown parameters,
are unknown univariate real functions, and
are independent random errors with mean zero, finite variances
and
a.s. Under some mild conditions, we present a sharp uniform-in-bandwidth limit law for the nonlinear additive components of the model estimated by the marginal integration device with the kernel method. We allow the bandwidth to varying within the complete range for which the estimator is consistent. We provide the almost sure simultaneous asymptotic confidence bands for the regression functions.
Acknowledgments
The author would like to thank the Editor-in-Chief, an Associate-Editor, and two referees for their extremely helpful remarks, which resulted in a substantial improvement of the original form of the work and a presentation that was more sharply focused.
CRediT author statement
Khalid Chokri: Conceptualization, Methodology, Investigation, Writing – Original Draft, Writing – Review & Editing.
Salim Bouzebda: Conceptualization, Methodology, Investigation, Writing – Original Draft, Writing – Review & Editing.
Both authors contributed equally to this work.
Disclosure statement
No potential conflict of interest was reported by the authors.